Self-similar solutions of equations of Korteweg -de Vries type

1980 ◽  
Vol 14 (3) ◽  
pp. 234-236 ◽  
Author(s):  
I. M. Krichever
Keyword(s):  
De Vries ◽  
Self Similar ◽  
Solutions Of Equations ◽  
Similar Solutions

scholarly journals Self-Similar Dynamics for the Modified Korteweg–de Vries Equation

2020 ◽  
Author(s):  
Simão Correia ◽  
Raphaël Côte ◽  
Luis Vega
Keyword(s):  
Vries Equation ◽  
Well Posedness ◽  
Critical Space ◽  
Asymptotic Description ◽  
De Vries ◽  
Self Similar ◽  
Similar Solutions

Abstract We prove a local well-posedness result for the modified Korteweg–de Vries equation in a critical space designed so that is contains self-similar solutions. As a consequence, we can study the flow of this equation around self-similar solutions: in particular, we give an asymptotic description of small solutions as $t \to +\infty$.

Self-similar solutions of equations of the nonlinear Schrödinger type

2000 ◽  
Vol 90 (3) ◽  
pp. 553-561 ◽  
Author(s):  
V. G. Marikhin ◽  
A. B. Shabat ◽  
M. Boiti ◽  
F. Pempinelli
Keyword(s):  
Nonlinear Schrödinger ◽  
Self Similar ◽  
Solutions Of Equations ◽  
Similar Solutions
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